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# Write an Equation When Given Its Solutions

## The calculator generates quadratic and cubic equations from its solutions using Vieta's formulas.

Enter solutions to the equation
Number of solutions

x1 =

x2 =

### Vieta's formulas

#### Write a Quadratic Equation When Given Its Solutions

If ${x}_{1}$ and ${x}_{2}$ are the roots of the quadratic equation ${\mathrm{ax}}^{2}+bx+c$ = $0$ then:
${x}_{1}+{x}_{2}$ = $-\frac{b}{a}$
${x}_{1} · {x}_{2}$ = $\frac{c}{a}$

If ${x}_{1}$ and ${x}_{2}$ are the roots of the quadratic equation ${x}^{2}+px+q$ = $0$ then:
${x}_{1}+{x}_{2}$ = $-p$
${x}_{1} · {x}_{2}$ = $q$

#### Write a Cubic Equation When Given Its Solutions

If ${x}_{1}$, ${x}_{2}$ and ${x}_{3}$ are the roots of the cubic equation $a{x}^{3}+b{x}^{2}+cx+d$ = $0$ then:
${x}_{1}+{x}_{2}+{x}_{3}$ = $-\frac{b}{a}$
${x}_{1}{x}_{2}+{x}_{1}{x}_{3}+{x}_{2}{x}_{3}$ = $\frac{c}{a}$
${x}_{1} · {x}_{2} · {x}_{3}$ = $-\frac{d}{a}$